Linear Logic was introduced by Girard as a resource-sensitive refinement of classical logic. It turned out that full propositional Linear Logic is undecidable (Lincoln, Mitchell, Scedrov, and Shankar) and, hence, it is more expressive than (modalized) classical or intuitionistic logic. In this paper we focus on the study of the simplest fragments of Linear Logic, such as the one-literal and con...

The simplex algorithm for linear programming is based on the fact that any local optimum with respect to the polyhedral neighborhood is also a global optimum. We show that a similar result carries over to submodular maximization. In particular, every local optimum of a constrained monotone submodular maximization problem yields a 1/2-approximation, and we also present an appropriate extension t...

the potential function of lippincott and schroeder for linear hydrogen bond has been re-examined and extended to nonlinear hydrogen bond. the parameters originally introduced to the potential function by lippincott and schroeder have been determined from the structural parameters such as 0.. .odistance 0-h bond distance, h.. .o distance and hoo angle. thevalidity of harmonic oscillator approxim...

the purpose of this study is to present an approximate numerical method for solving high order linear fredholm-volterra integro-differential equations in terms of rational chebyshev functions under the mixed conditions. the method is based on the approximation by the truncated rational chebyshev series. finally, the effectiveness of the method is illustrated in several numerical examples. the p...

in this paper, we propose a new method for solving the stochastic advection-diffusion equation of ito type. in this work, we use a compact finite difference approximation for discretizing spatial derivatives of the mentioned equation and semi-implicit milstein scheme for the resulting linear stochastic system of differential equation. the main purpose of this paper is the stability investigatio...

In this paper, we present approximation algorithms for the directed multi-multiway cut and directed multicut problems. The so called region growing paradigm [1] is modified and used for these two cut problems on directed graphs By this paradigm, we give for each problem an approximation algorithm such that both algorithms have an approximate factor. The work previously done on these problems ne...

Multi-layer feedforward neural networks with sigmoidal activation functions have been termed "universal function approximators". Although these types of networks can approximate any continuous function to a desired degree of accuracy, this approximation may require an inordinate number of hidden nodes and is only accurate over a finite interval. These short comings are due to the standard multi...

We are grateful that Hastie points out the connection to degrees of freedom for LARS which leads to another—and often better—definition of degrees of freedom for boosting in generalized linear models. As Hastie writes and as we said in the paper, our formula for degrees of freedom is only an approximation: the cost of searching, for example, for the best variable in componentwise linear least s...